Figure 10

Optimal scalable TLR scheme for the surface code. The problem is first solved for the couplings between qubits of unit cell 0 and the rest of the lattice, and then we have translated the result to cover the whole lattice. This results is equivalent to the one originally proposed in Ref. [13]. The TLRs are represented by solid lines and the squares denote the starting and ending points of TLRs. Note that rotating each individual four-qubit TLR by 90 degrees leads obviously to another optimal solution. The two-qubit TLRs on the edges and the three-qubit TLRs on the corners (purple) have been put by hand, since a full optimization solution of a smaller surface code lead to such a pattern of boundary two- and three-qubit TLRs. Indeed, it seems clear that this solution at the boundaries remains optimal for a larger surface code.